I've always figured it wasn't the ODDS that mattered, so much as the STAKES.
It's both and more.
If the stakes are negligible then it doesn't make sense to spend a lot of time/money/effort preparing for that situation regardless of the odds.
But when the stakes are large then you have to weigh the odds, your ability to make a difference and the amount of time/effort/money you can/are willing to spend.
For example, the stakes of an airliner falling on my house are huge, but the odds are astronomically small. I could protect my house by encasing it in a concrete/steel dome like they use to protect nuclear reactors, but it would take a huge amount of time/effort/money.
Given the tiny odds and the tremendous difficulty in making a difference I choose not to prepare for this event even though the stakes are tremendous.
Now, let's say that tomorrow a device comes on the market that sells at any Wal-Mart for $2.99, that plugs into a standard outlet and emits a forcefield that repels all falling aircraft. Now the time/effort/money required to protect my house is virtually nil so I might spring for the $3 even though the odds and stakes haven't changed.
Let's say that I'm worried about an asteroid hitting my house. Now nothing I can do will make a difference so the odds & stakes don't matter a bit.
Ok, for a more practical example let's look at carrying a handgun.
The odds of having to use deadly force in self-defense are quite small, but the stakes are quite large. It's a situation where the statistics show it's very likely one can improve his chances of a successful outcome if he has a handgun available.
Scenario 1: I hate guns, am on a very limited income, am allergic to steel and live in a place where guns are difficult to purchase and impossible to carry. Conclusion? I don't want a handgun, don't have the money for one, would have a hard time buying one if I wanted, it would make me sick to touch it and I couldn't carry it no matter what. So regardless of the stakes, the odds and the fact that I COULD make a difference if I had a handgun I'm not going that direction. The time/effort/money/illegality required to make it happen render the solution infeasible. So instead I buy a squirt gun and fill it with lemon juice to spray in the attacker's eyes.
Scenario 2: I shoot handguns for competition, already have a concealed carry permit because it simplifies purchases and transporting firearms and I can buy the perfect carry pistol & hoslter for less than my take-home pay from a single day of work. Now carrying a handgun looks very attractive although the stakes & odds haven't changed a bit.